Visual positioning system for marine industrial robot assembly based on complex variable function

Gravitational field exists in three-dimensional space. If the distribution of a known field is independent of some coordinate, it can be reduced to a two-dimensional field. Such field is called plane scalar field. In practical problems, there are many two-dimensional field problems, and the exact solution can be obtained by analysing two-dimensional field in complex plane by using the theory of complex variable function. In this paper, the application of complex function theory in gravitational field is discussed. In a rectangular coordinate system, if the plural z in the continuous change of the region in a complex plane, if f (z) as analytic function, it is the real part and imaginary part of cauchy Riemann equation; if only for the xy plane changes in the gravitational field, and the z axis perpendicular to the x-y plane direction does not change, that field is called a parallel plane; the gravitational field of the equipotential surface is parallel to the bus in Oz axis of the cylindrical surface, but in xoy plane, curve equation is shown in Figure 1 [5–7]. The cylinder in the three-dimensional space will be represented as a two-dimensional image in the image, which can be restored through two parallax images. However, in the actual process, the complex shape obstacles detected by the image are not regular graphs. In this paper, the minimum enclosing circle method is adopted, that is, by fitting the minimum enclosing circle of the obstacle image, the localisation of obstacles is realised. The core of obstacle localisation is to obtain the minimum enclosing circle in the image, which is the model of the minimum enclosing circle of any shape.

Robot is widely used in various aspects of life, production accessories and simple reproduction are widely used and the use of robots is people’s pursuit of high quality life of the first and most important step; therefore the means to formulate the visual Angle of industrial robot assembly is the duty of every staff engaged in this task. Therefore, as an important technical index of assembly system, assembly precision directly determines the performance of the whole system. It combines the complex function and uses the visual positioning method to achieve the target object position measurement. By introducing visual positioning technology to the industrial robot, the position information of the target point to be moved to can be obtained by the industrial robot without teaching. However, the motion trajectory of the industrial robot from the starting point to the target point cannot be determined. Therefore, the means to make the robotic arm avoid obstacles and solve the obstacles’ avoidance in the assembly process is a key problem.

Fig. 1

There are many ways of obstacle avoidance path planning for the robotic arm. According to the motion form of obstacles, it can be divided into static obstacle avoidance path planning and dynamic obstacle avoidance path planning. From the perspective of workspace, it can be divided into global path planning and local path planning. Generally, the global path planning environment is completely known, while the local path planning environment is partially known or completely unknown. Artificial potential field makes path planning for obstacle avoidance of the robot arm, and defines the working environment of the robot arm as an abstract potential field [8]. The gravitational field function between the target point and the end of the manipulator is defined as follows: (1) Uatt(q)=12ξρ2(q,qgoal) Where the gravitational field coefficient constant ξ is >0, the q represents the current position coordinate at the end of the manipulator; q_goai represents the position coordinate of the target point.

The negative gradient of the complex function of gravitational field is the gravitational function: (2) Fatt(q)=−∇Uatt(q)=ξ(qgoal−q) Define repulsion field functions: (3) Urep(q)={ 12η(1ρ(q,qobs)−1ρ0)2,ρ(q,qobs)≤ρ00,ρ(q,qobs)>ρ0 The negative gradient of repulsive field complex function is repulsive function: (4) Frep(q)=−∇Urep(q){ η(1ρ(q,qobs)−1ρ0)1ρ2(q,qobs),ρ(q,qobs)≤ρ00,ρ(q,qobs)>ρ0 Therefore, in the virtual artificial Potential field, the resultant force of the robot is: (5) F(q)=Fatt(q)+Frep(q) If the target point is far away from the manipulator, the gravity function can be modified to increase the range limit. By introducing threshold d*_goal, the distance between the target point and the end of the manipulator can be limited, and the gravity is too large because it is too far from the target point. The modified gravitational field function is as follows: (6) Uatt(q)={ 12ξρ2(q,qgoal),ρ(q,qobs)≤dgoal*dgoal*ξρ2(q,qgoal)−12ξρ2(dgoal*)2,ρ(q,qobs)>dgoal* The corresponding gravitational function is: (7) Fatt(q)=−∇Uatt(q)={ ξ(qgoal−q),ρ(q,qobs)≤dgoal*dgoal*ξ(qgoal−q)ρ(q,qobs)−ρ(q,qobs)>dgoal* When there are obstacles in the attachment of the target point, the problem that the manipulator can not reach the target point can be solved by modifying the repulsion field function, adding the influence of the distance between the target and the end of the manipulator on the basis of the original repulsion force. The modified repulsion field function is as follows: (8) Uatt(q)={ 12ξρ2(q,qgoal),ρ(q,qobs)≤dgoal*dgoal*ξρ2(q,qgoal)−12ξρ2(dgoal*)2,ρ(q,qobs)>dgoal* The corresponding repulsion function becomes: (9) Frep(q)=−∇Urep(q)={ η(1ρ(q,qobs)−1ρ0)ρn(q,qobs)ρ2(q,qobs)+n2η(1ρ(q,qobs)−1ρ0)2ρn−1,ρn(q,qobs)≤ρ00,ρ(q,qobs)>ρ0 The gravitational potential energy function of the virtual target point can be represented by a quadratic function:(10) Evir=kvir[−(d−μ)2+μ2] The flux function v and allele function in the electric field u satisfy the Laplace equation. Therefore, the complex function can be directly introduced to study the modified gravitational field function.

The whole assembly system is mainly divided into two parts, namely the vision processing part and the robot motion control part. The visual processing part is responsible for obtaining the location and size information of target objects and obstacles in the working environment. The motion control part of the robot realises the motion control of the industrial mechanical arm and the execution of assembly tasks. The workflow of the whole system is shown in Figure 2.

According to the overall scheme design of the system, the visual system in this paper includes binocular vision system and monocular vision system, and adopts camera for image acquisition. In the application of machine vision system, industrial cameras are usually used for image acquisition, and the resolution, focal length, aperture, interface, depth of field and other factors need to be considered when selecting cameras and lenses. For the binocular vision system responsible for coarse positioning in the system, the camera is fixed on the bracket. When selecting the camera and lens, it should be noted that all parameters of the left and right cameras and lenses are exactly the same. For the monocular vision system in the system, which is responsible for precise positioning, the camera is fixed at the end of the robot arm, and its main function is to achieve accurate positioning of the two-dimensional information of the target. In the process of selecting industrial robots, it is necessary to take into account the factors such as the degree of freedom, repeatable positioning accuracy, load and motion range of industrial robots. The system structure of the industrial robot is composed of a sensing system, a control system, a driving device, a transmission device and an actuator, as shown in the structural form of the industrial robot [9].

Fig. 2

Marine industrial robot collaborative assembly is mainly used in Marine industrial robot collaborative handling operations. The experimental task is: the Marine industrial robot moves the experimental object, moving the object from the starting point to the end point. It is known that the motion path of the experimental robot is an arc with a diameter of 10 cm and the rotation Angle is 120°. The experimental steps are as follows, as shown in Figure 3. Step 1: Establish the cooperative motion system model of Marine industrial robots, and set three feature points (A, B, c) in the virtual object coordinate system. Step 2: According to the task requirements of cooperative handling rigid objects, the constraint matrix of tool coordinate system of Marine industrial robots is listed. Step 3: The path constraint model is established according to the constraint matrix relation, so that the contour of the path model satisfies the constraint relation at every point. The path model is established as shown in Figure 4.

Step 4: Pick up the inside and outside arc contours X and Y of the path model as the trajectory information, and adjust the path through the path rotation and translation command, so that the path satisfies the constraint matrix, and analyse the results.

Step 5: Calibrate the object coordinate system of the Marine industrial robot. The offline trajectory of the Marine industrial robot is transformed into the actual trajectory according to the transformation matrix.

Step 6: Manually adjust the Marine industrial robot.

Fig. 3